Chapter 5 Practice Problem Answers 1.

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1 hapter 5 Practice Problem nswers 1. raw the Quadrilateral Family Venn iagram with all the associated definitions and properties. aroody Page 1 of 14

2 Write 5 ways to prove that a quadrilateral is a parallelogram: hapter 5 Practice Problem nswers 1. oth pairs of opposite sides of a quadrilateral are parallel oth pairs of opposite sides of a quadrilateral are congruent One pair of opposite sides of a quadrilateral are both parallel and congruent The diagonals of a quadrilateral bisect each other oth pairs of opposite angles of a quadrilateral are congruent Name 5 properties of a rectangle that is not a rhombus and the corresponding properties of a rhombus that is not a rectangle: 1. Rhombus that is not a Rectangle iagonals are Rectangle that is not a Rhombus iagonals are not iagonals bisect the s iagonals do not bisect the s ll 4 sides are Not all 4 sides are (only opposite sides are ) No right s t least 1 right (actually, all s are right!) iagonals are not iagonals are aroody Page 2 of 14

3 Give the best name for a quadrilateral whose: hapter 5 Practice Problem nswers 1. onsecutive sides measure 15, 18, 15, 18 Parallelogram onsecutive sides measure 15, 18, 18, 15 Kite onsecutive s measure 30, 150, 110, 70 Trapezoid iagonals are and and bisect each other quare iagonals bisect each other and bisect the s Rhombus nswer ometimes, lways, or Never 1. If the diagonals of a quadrilateral are, it is an isosceles trapezoid. ometimes If the diagonals of a quadrilateral divide each such that each half measures 45, the quadrilateral is a square. lways If a parallelogram is equilateral, it is equiangular. ometimes If 2 s of a trapezoid are, the trapezoid is isosceles. ometimes aroody Page 3 of 14

4 6. is a parallelogram. Find the measure of. hapter 5 Practice Problem nswers x+24 ( x+24) + ( 2x+6) = 180 x = 50 2x+6 m = m = 2( 50) + 6 = is a rectangle. The area is 160 u 2. Find the perimeter. x( x+6) = 160 x 2 + 6x = 0 x ( x + 16) ( x - 10) = 0 x = -16 and/or x = 10 x+6 an't be -16 as this makes < 0 x = 10 and P = 52 u aroody Page 4 of 14

5 8. hapter 5 Practice Problem nswers P O NR P N OP is isosceles O R 1. O ON OR ONR ORN NR P ONR P 6. ORN 6. P 7. P 7. Transitive Property of s 8. OP O 8. onverse of ITT 9. OP is isosceles 9. efinition of Isosceles ll radii of a ITT P are 9. supp. supp. 1. supp. supp. IP PI aroody Page 5 of 14

6 10. hapter 5 Practice Problem nswers Y Y YZ Y YZ bisects Y Z 1. Y Y Y ITT YZ ZY P Y YZ PI 6. ZY YZ 6. Transitive Property of s 7. YZ bisects Y 7. efinition of bisector 11. O O 1. O O O raw O & O O O O O O O 7. PI 8. O O 8. PI 9. O O 9. Transitive Property of s 10. O O 10. ( 2, 8, 4) PT ll radii of a uxiliary Lines ll radii of a ITT are are aroody Page 6 of 14

7 1 hapter 5 Practice Problem nswers is an isosceles trapezoid with legs & P P & 7. P P 7. onverse of ITT 8. P P P are isosceles 1. is an isosceles trapezoid with legs & ubtraction Property of egments 9. P & P are isosceles 9. efinition of Isosceles 8. Reflexive Property ( 2, 3, 4) 6. P P 6. PT efinition of Legs of Isos. Trapezoid iagonals of an Isos. Trap. are 1 is a E F F G bisects EF E 1. is a FE EF 6. E F F E 7. ubtraction Property of egments 8. FG EG 9. GF GE PT 10. bisects EF 10. efinition of egment isector efinition of a PI PI Opposite sides of a are ( 3, 7, 4) aroody Page 7 of 14

8 1 hapter 5 Practice Problem nswers is a GH FE H E G E F GH EF H 1. is a H E H E GH FE efinition of PI 8. GH FE 8. ( 5, 4, 7) 9. GH EF 9. Opposite sides of a are ubtraction Property of egments PT 1 I I bisects R I IR K R IR is a kite 1. I bisects R K KR I IR I bis. R IR is a kite efinition of egment isector E.T. ( 2,3) If one diagonal of a quadrilateral is the bis. of the other, then the quadrilateral is a kite aroody Page 8 of 14

9 hapter 5 Practice Problem nswers 16. YTWX is a YP TW ZW TY TP TZ Z Y X YTWX is a rhombus T P W YTWX is a YP TW ZW TY YPT & WZT are right s efinition of segments YPT WZT RT 6. TP TZ YTP WTZ 7. Reflexive Property 8. YTP WTZ 9. YT WT ( 5, 6, 7) PT 10. YTWX is a rhombus 10. If a has 2 consecutive sides, it is a rhombus F is a F E F E FE is a 1. F is a F F E F E 6. F E 6. PT 7. F 7. Opposite sides of a are 8. E PT 9. FE 9. ubtraction Property of egments 10. FE is a 10. If a quadrilateral has both pairs of opposite sides, it is a 8. Opposite sides of a are Opposite s of a are ( 3, 2, 4) aroody Page 9 of 14

10 hapter 5 Practice Problem nswers 18. is a E E is isosceles 1. is a is right efinition of segments is a rectangle with at least one right is a rectangle & bisect each other The diags of a bisect each other 6. E is the midpoint of & 6. efinition of egment isector The diagonals of a rectangle are 8. E E 8. ivision Property of egments 9. E is isosceles 9. efinition of Isosceles 19. E & E are isosceles with bases &, respectively E is a rectangle 1. E & E are isosceles with bases &, respectively E E; E E E E E E 6. is a parallelogram is a rectangle efinition of Isosceles VT ( 2, 3, 2) PT 6. If a quadrilateral has two pairs of opposite sides, it is a parallelogram 7. ddition Property of egments 8. If a parallelogram has diagonals, it is a rectangle aroody Page 10 of 14

11 hapter 5 Practice Problem nswers 20. Prove that the quadrilateral formed by connecting the midpoints of the sides of a is a. H is a E, F, G, & H are midpoints E G EFGH is a F 1. is a ; E, F, G, & H are midpoints E G; H F; H F; E G ; The opposite s of a are 6. EH GF; HG FE 6. ( 4, 5, 4) 7. EH GF; HG FE 7. PT 8. is a 8. quadrilateral with both pairs of opposite sides is a The opposite sides of a are ivision Property of egments 21. TWX is isosceles with base WX RY WX T RWXY is an isosceles trapezoid W R Y X 1. TWX is isosceles with base WX TW TX W X RY WX RWXY is a trapezoid 6. RWXY is an isosceles trapezoid 6. trapezoid with lower base s congruent is isosceles efinition of Isosceles ITT efinition of Trapezoid aroody Page 11 of 14

12 hapter 5 Practice Problem nswers 2 EFGH is a E F G H H E G is a F 2 1. EFGH is a EF GH; HE FG E F G H F H; E G ddition Property of egments FEH HGF; GHE EFG The opposite s of a are 6. FG, GH, HE, & EF 6. ssumed from diagram are straight angles 7. EFG supp. F; 7. If 2 s form a straight, they are supp. GHE supp. H; HEF supp. E; FGH supp. G 8. E G; F H 8. upps. of s are 9. F H; G E 9. ( 3,8,4) 10. ; 10. PT 11. is a 11. quadrilateral with both pairs of opposite sides is a ROT is a parallelogram M TP The opposite sides of a are R T P MOPR is a parallelogram M O 7. RTM OP 7. ( 3, 5, 6) 8. RM PO 1. ROT is a M TP 9. TMR PO PT PT 10. RM PO 10. IP 11. is a 11. quadrilateral with one pair of opposite sides both & is a aroody Page 12 of MT P ddition Property of egments RT O efinition of RT OT PI 6. RT O 6. The opposite sides of a are

13 2 hapter 5 Practice Problem nswers PQR is a is the midpoint of QR Q R P bisects QP bisects PR P 1. PQR is a P bisects QP QP P QR P efinition of QP P PI 6. QP QP 6. Transitive Property of s 7. Q QP 7. onverse of ITT 8. QP R 8. Opposite sides of a are 9. is the midpoint of QR 10. Q R efinition of Midpoint 11. R R 11. Transitive Property of egments 1 R R 1 ITT 1 R P 1 PI 1 R P 1 Transitive Property of s 1 bisects PR 1 efinition of bisector efinition of bisector aroody Page 13 of 14

14 2 KOR is equilateral KOPR is a KMOR is a hapter 5 Practice Problem nswers J K R JMP is equilateral M O P 1. KOR is equilateral KO KR RO KMOR is a JM RO KOPR is a 6. JP KO 6. efinition of 7. JKOR is a 7. efinition of 8. KM RO; MO KR 8. Opposite sides of a are 9. RP KO; OP KR 9. Opposite sides of a are 10. JK RO; JR KO Opposite sides of a are 11. JK KM MO OP JR RP 11. Transitive Property of egments 1 JM MP JP 1 ddition Property of egments 1 JMP is equilateral 1 efinition of Equilateral 10. efinition of Equilateral efinition of aroody Page 14 of 14

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